B757 CREW HAD AN ALTDEV IN ZID CLASS A AIRSPACE. THE CTLR SLOWED THE ACFT TO 250 KTS. IN RESPONSE; THE CREW DSNDED TO FL250.

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ALTDEV. I WAS THE PNF AND WAS USING ACARS TO CONTACT DISPATCH TO CLARIFY A NOTAM/APCH FIX QUESTION REGARDING A HOLDING FIX CHANGE ON MISSED APCH -- NOTAM SPELLED FIX BETHY/APCH PLATE SPELLED BATHY. FLT ATTENDANTS CALLED IN THE MIDST OF THE APCH BRIEFING REQUESTING: 1) INBOUND GATE INFO; 2) TEMP COMPLAINT IN THE BACK; AND 3) CONNECTING INFO. ATC (ZID) WAS GIVING US MULTIPLE SPD; ALT; AND HDG CHANGES. SOMEHOW 'CROSS JOUNN AT 350 KTS' WAS TRANSLATED BY US TO 'CROSS JOUNN AT FL250.' WE; AS A CREW; ARE CONSCIENTIOUS ABOUT VERIFYING THE ALT WINDOW SETTING BUT SOMEHOW MANAGED TO MISS IT THIS TIME. DISTRS WERE OBVIOUSLY A FACTOR BUT FLT ATTENDANTS OR DISPATCH SHOULD NOT DISTRACT A PLT FROM FLYING FIRST. SUPPLEMENTAL INFO FROM ACN 596996: FLT ZZZ TO CVG; IFR FLT PLAN. ARR TO CVG WITH ZID MULTIPLE RADAR VECTORS GIVEN AND ALT CHANGES TO SLOW AND SEQUENCE TFC TO CVG. IN PREPARATION FOR APCH NOTAM REVIEW BROUGHT DISCREPANCY TO OUR ATTN AND WE WERE TALKING WITH DISPATCHER TO CONFIRM NOTAM. ALSO; FLT ATTENDANTS RANG (CALLED) THE COCKPIT 3 TIMES WITH REQUESTS FOR GATES; TEMP AND OTHER REQUESTS. ALL THIS AT THE SAME TIME WE WERE BEING GIVEN ALT AND AIRSPD CHANGES AND RESTRS. COCKPIT WAS BUSY BUT PROCS WERE BEING USED AND FOLLOWED. AT 20 NM NW OF JOUNN INTXN; ATC GAVE WHAT I HEARD WAS ALT CHANGE TO FL250. (WE WERE PRESENTLY AT FL290.) I HEARD CTLR SAY 'TWO; FIVE; ZERO' -- INDICATING ALT CHANGE AS OPPOSED TO TWO HUNDRED AND FIFTY (INDICATING SPD CHANGE). CAPT (PNF) WAS VERY BUSY WITH OTHER DISTRS AND STILL OPERATING RADIOS. I DO NOT RECALL HIS READBACK. CAPT REMEMBERS READING BACK 'TWO HUNDRED FIFTY.' IN THE MIDST OF ALL THAT WAS GOING ON; OUR VERIFICATION WAS NOT ACCOMPLISHED. WE DSNDED TO CROSS JOUNN AT FL250.